Question
Download Solution PDFनिम्नलिखित डेटा, 46, 34, 22, 26, 14, 20, 16 और 44 के लिए माध्य विचलन ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
असमूहीकृत डेटा के लिए माध्य विचलन:
'n' अवलोकन x1, x2 ………… .. xn के लिए उनके माध्य \(\bar x\) के ओर विचलन इसके द्वारा दिया गया है: \(M.D= \frac{{\mathop \sum \nolimits_{i = 1}^n \left| {{x_i} - \bar x} \right|}}{N}\) जहां N अवलोकनों की संख्या है
गणना:
दिया गया संख्याओं का डेटा 46, 34, 22, 26, 14, 20, 16 और 44 हैं।
माध्य \(\bar x = \frac{{Sum\;of\;all\;the\;observations}}{{Total\;number\;of\;observations}} = \frac{{46\; +\; 34\; + \;22\; + \;26\; + \;14\; + \;20\; + \;16\; + \;44}}{8} = 27.75\)
∴ माध्य विचलन\( = \frac{{\left| {46 - 27.75} \right| + \left| {34 - 27.75} \right| + \left| {22 - 27.75} \right| + \left| {26 - 27.75} \right| + \left| {14 - 27.75} \right| + \left| {20 - 27.75} \right| + \left| {16 - 27.75} \right| + \left| {44 - 27.75} \right|}}{8}\)
⇒ माध्य विचलन = \(\frac{{81.5}}{8} \) = 10.18
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